The distance of a point from a line Ax+By+C=0 is $\displaystyle \lvert\frac{Ax+By+C}{\sqrt{A^2+B^2}}\rvert$

I took a point on the line (x,y) and any other point (x1,y1). I wrote the distance between them and replaced y with an expression of x using the equation of the line.

Then i differentiated the expression to find the minimum distance. I got this

Bx - Bx1 + A ( y1 + (Ax + c)/B ) divided by sqrt ( B^{2}(x1-x)^{2}+ (By1 + Ax + c)^{2})

What now?